Multivariate Normal Distribution

#1

Why did we calculate the probability density function(P(X)) and how is it derived?

#2

For an intutive idea about probability distributions check out these blogs :
https://mathinsight.org/probability_distribution_idea
https://mathinsight.org/probability_density_function_idea

For the derivation you can check out this pdf :
http://noahgolmant.com/writings/derivationsunivariatemultivariate.pd